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WASHINGTON — A Republican invitation for Israel’s prime minister, Benjamin Netanyahu, to address Congress next month is highlighting the tensions between President Obama and Netanyahu and has kicked off a bizarre diplomatic race over who will be the first to lay out a new proposal to reopen the stalled Israeli-Palestinian peace talks.

For three months, White House officials have been debating whether the time has come for Obama to make a major address on the region’s turmoil, and whether he should use the occasion to propose a new peace plan for Israelis and Palestinians.

One administration official said that course is backed by Secretary of State Hillary Rodham Clinton and the president himself, but opposed by Dennis B. Ross, the president’s senior adviser on the Middle East.

Netanyahu, fearful that his country would lose ground with any Obama plan, has been considering whether to preempt the White House with a proposal of his own in front of a friendly Congress, according to US officials and diplomats from the region.

“People seem to think that whoever goes first gets the upper hand,’’ said Daniel Levy, a former Israeli peace negotiator.

The political gamesmanship illustrates how the calculation in the Middle East has changed for a variety of reasons, including the upheaval in the Arab world. But it also shows the lack of trust between Obama and Netanyahu.

White House officials are working on drafts of a possible proposal. If Obama does put forward a plan, officials said it could include four principles, or terms of reference, built around final status issues that have bedeviled peace negotiators since 1979.

The terms of reference could call for Israel to accept a Palestinian state based on the 1967 borders. For their part, Palestinians would have to accept that they would not get the right of return to land in Israel from which they fled or were forced to flee. Jerusalem would be the capital of both states, and Israeli security would have to be protected.

The tussling between the Obama administration and the Israeli government reached a peak last week when Clinton, in Qatar, announced that Obama would soon be “speaking in greater detail about America’s policy in the Middle East and North Africa.’’

Her announcement electrified Israeli officials, who quickly got on the phone with US officials to determine whether Obama had decided to put an American plan on the table. White House officials cautioned that the internal debate was still going on.

But two days later, the House speaker, John A. Boehner of Ohio, announced plans to invite Netanyahu to address Congress.